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Pregled bibliografske jedinice broj: 538406

Časopis

Autori: Feretić, Svjetlan; Guttmann, Anthony J.
Naslov: Polyominoes with nearly convex columns: An undirected model
( Polyominoes with nearly convex columns: An undirected model )
Izvornik: Glasnik matematički (0017-095X) 45 (2010), 2; 325-346
Vrsta rada: članak
Ključne riječi: polyomino; hexagonal cell; nearly convex column; area generating function; growth constant
( polyomino; hexagonal cell; nearly convex column; area generating function; growth constant )
Sažetak:
Column-convex polyominoes were introduced in 1950's by Temperley, a mathematical physicist working on ``lattice gases''. By now, column-convex polyominoes are a popular and well-understood model. There exist several generalizations of column-convex polyominoes. However, the enumeration by area has been done for only one of the said generalizations, namely for multi-directed animals. In this paper, we introduce a new sequence of supersets of column-convex polyominoes. Our model (we call it level m column-subconvex polyominoes) is defined in a simple way: every column has at most two connected components and, if there are two connected components, the gap between them consists of at most m cells. We focus on the case when cells are hexagons and we compute the area generating functions for the levels one and two. Both of those generating functions are q-series, whereas the area generating function of column-convex polyominoes is a rational function. The growth constants of level one and level two column-subconvex polyominoes are 4.319139 and 4.509480, respectively. For comparison, the growth constants of column-convex polyominoes, multi-directed animals and all polyominoes are 3.863131, 4.587894 and 5.183148, respectively.
Projekt / tema: 177-0000000-0884, 037-0000000-2779
Izvorni jezik: eng
Rad je indeksiran u
bazama podataka:
Scopus
SCI-EXP, SSCI i/ili A&HCI
Science Citation Index Expanded (SCI-EXP) (sastavni dio Web of Science Core Collectiona)
Kategorija: Znanstveni
Znanstvena područja:
Matematika
Puni text rada: 538406.glasnik_2010_page_proofs.pdf (tekst priložen 13. Stu. 2011. u 20:36 sati)
URL Internet adrese: http://web.math.hr/glasnik/vol_45/no2_03.html
Broj citata:
Altmetric:
DOI: 10.3336/gm
URL cjelovitog teksta:
Google Scholar: Polyominoes with nearly convex columns: An undirected model
Upisao u CROSBI: svjetlan.feretic@gradri.hr (svjetlan.feretic@gradri.hr), 13. Stu. 2011. u 20:36 sati



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